Report Number: CS-TR-77-604
Institution: Stanford University, Department of Computer Science
Title: Control of the dissipativity of Lax-Wendroff type methods for first order systems or hyperbolic equations
Author: Chan, Tony Fan C.
Author: Oliger, Joseph
Date: March 1977
Abstract: Lax-Wendroff methods for hyperbolic systems have two characteristics which are sometimes troublesome. They are sometimes too dissipative -- they may smooth the solution excessively -- and their dissipative behavior does not affect all modes of the solution equally. Both of these difficulties can be remedied by adding properly chosen accretive terms. We develop modifications of the Lax-Wendroff method which equilibrate the dissipativity over the fundamental modes of the solution and allow the magnitude of the dissipation to be controlled. We show that these methods are stable for the mixed initial boundary value problem and develop analogous formulations for the two-step Lax-Wendroff and MacCormack methods.